•Soil deformation during tunnel excavation is conducted in heavy rainy weather.•Modified Green-Ampt model with assumption of soil stratification is adopted.•Complex variable approach is introduced to evaluate tunnel structural construction.•Analytical solutions for ground responses are compared with observed data.•Parametric analysis are performed for influence of sensitive parameters of rainfall. The evaluation of influence of heavy rainfall on tunnel structural construction is a problem being faced by engineers around the world. Current analytical solutions on the tunnelling-induced ground movements are generally based on the normal sunny weather and provide little attention on the rainfall intensity and duration risk. In this paper, a time-dependent complex variable approach is proposed to estimate the deformation and stress of surrounding soils caused by tunnelling considering the rainfall infiltration mechanisms. The modified Green-Ampt model under the assumption of stratification is used to simulate the rainfall infiltration process and the complex function theory is employed to calculate the subregion mapping for the saturated, transitional, and natural layers. The non-uniform convergence deformation boundary is adopted at the tunnel structure opening so as to consider the displacement controlled excavation effects due to tunnelling. The analytical presented solution is then verified by comparisons with a total of three engineering case records. It is revealed that the presented complex variable solution considering the rainfall infiltration mechanism can provide a prediction of surface settlement, soil subsidence and horizontal displacement in good agreements with the field measurements. Finally, the parameters that affect the ground deformation and stress induced by tunneling in rainy day, including the rainfall intensity, saturated permeability, matric suction, initial water content, are studied. The paper contributes to provides a relatively quick and easy way of accurately evaluating the time-dependent feedback in tunnel-soil interaction system involving heavy rainfall as a potential risk in the preliminary design of tunnel structures considering the adverse weather condition.